Brilliant question... Is it as important that the theory makes a contribution to society as it is that more than one person understands it? Are these criteria mutually exclusive?

I would suggest that it is possible to make a contribution to society with a theory that nobody except its creator understands

I suppose my proposition is based on the premise that the theory can be realised in practice by the creator:

A unique mind cracks cold fusion, or say, inter-stellar travel and can provide the practical outlay, or at least the derivative equations for the technology's design. If so, it wouldn't necessarily matter that no one else understands the underlying theory, only that they can build the technology according to those derivative equations that are within the intellectual capabilities of her/his peers

Well yes, indeed. I don't think there are any concrete examples but I hope that it is only a matter of time before another intellect like Da Vinci arrives.... :)

The act of creating and validating science is anthropocentric. First, a scientific result of one creator must pass a review team in order to be published. The definition of "acceptability" (of a scientific theory) itself involves the requirement of review from other scientists. And this review team is at its turn a representative of a larger scientific community. Acceptability cannot be defined and employed outside humans and without majority criteria. This is the way things works in science, as in other human fields. Of course, over time a theory can prove to be inconsistent, false or improvable from its very foundations, and history of science offers plenty of such examples. The new theory again takes the place of the outdated one by the vote of (other) scientists. There are no universal criteria to judge science. Maybe God has them. Minds are individual and mind can change, it is in human nature.

In your example with extraterrestrials:

1) We cannot know that communication with them is impossible.

2) You already assume their "science". If you stay with two notions of science, their and ours, your question gets a NO (science is not limited to humans). If you stay with one notion of universal science (either non-communicable or communicable between species) the answer remains NO.

I do not think this example is relevant for your intial question, as the same problem could be posed within that extraterrestrial community.

There are three aspects:

1)The acceptance among the specialists (as was written above from Artur, by referees), which probably will not take place until the end of author's life, sometimes.

2)The agreement with laboratory experiments, which can be checked using raw data

3)The understanding from well scientifically educated people

If one of the above fails, then no success.

There are of course some objections about the 3rd one, but, imho, it is a matter of time to overcome them...

Dear Marcel, your question is interesting because of the so many hidden theories.

I don't know, probably the peer-review process is a 'closed profession' practise and do not improve in the long term our knowledge. You see, if you want a formal success, then you have to follow the traditional way, to be a good guy, accept everything the 'wise people' have written (even they seem to be simple nonsenses) and try to do a small change in the main presentation: That's the end and no step forward. So, the main theory is carrying out like a Religion Text, no major modifications are allowed!

As long as I am thinking I tend to believe that now, instead of one Rome and one Vatican, we just have a pleiad of 'Romes' and 'Vaticans', but the mentality is the same and many times worse...

I completely agree with Atur. If a theory cannot be understood by others and related or hypothesis cannot be tested, it fails a theory's very important test: reproducibility.

@ Dear Marcel, you are right to point certain theories of origin of the Universe, but even superstring theory about which "Scientists have joked about how string theory is promising... and always will be promising, for the lack of being able to test it," has some experimental evidence in its favour:

http://phys.org/news/2014-01-scientists-theory.html

As far as big bang theory is concerned, it not only explains several of observable phenomena in the universe, evidence for it comes now and then. Therefore, the argument of Demetris cannot be so lightly done away.

Dear Marcel,

I do agree with you.. But, if a theory is not comprehended by others how one claim that prediction by one's theory is correct unless someone else using the same theory find out that perdition is correct. Such a theory will remain with its creator and cannot be put to use. As far as your above response is concerned, I am aware that history of science is replete with instances wherein several competing and better theories were sacrificed on the alter of simplicity and compatibility with the scientific structure in practice.

Dear Marcel,

I understand that there has always linguistic problem in scientific communication. Of course, it becomes sometimes difficult to understand a theory given by someone in his/her mother tongue. A language and its expressions, even living amongst native over the years cannot be comprehended fully. I do not mean that science is not universal, but product of culture. I am talking about the subtlety of expression in different language. But, it is not necessary that science can be done only in English. But, since at present English is the international language of science communication, therefore, one who proposes a theory should for wider audience for the welfare of humanity, get one theory translated by a native English-speaking scientist in the same branch of science so that if there is a doubt or confusion must be cleared by the proponent of the theory then and there. It is interesting to note irrespective of the fact whether we think using language or not, the first expression of thought, even of those well-versed in Englishish and studying and teaching in English speaking countries, is generally is in their native language in their unconscious mind and a translated version into English into the conscious mind.

Dear Marcel,

Further, there arises no language problem, if "one bright person truly understands that theory (e.g. the creator of a theory)? ".

If no person of the same branch of knowledge and speaking the same language cannot comprehend the theory, how can it be falsified or accepted by the scientific community? Is the person in question dumb?

I think everyone is being much too narrow here. I see no reason why a particularly powerful mind should not arrive at a theory that nobody else understands but which nevertheless provides useful and reliable predictions. Many people have published theories in book form, which requires no editor or peer review.

I am not sure whether historically there has ever been such a case but I do not see any objection in principle. The theory of conservation of energy might provide an example if anyone really knew the historical facts. Leibniz may be credited with this, although there were English physicists who may have reached it first on empirical grounds. What may be different about Leibniz is that he reached the theory on a priori logical grounds as part of a view of reality that I think it is fair to say absolutely nobody claims to understand in full. Most people regard Leibniz's view of reality as absurd. Others see considerable insight in some of his proposals. Nobody I have ever met can comprehend his overall schema. Yet this schema threw up all sorts of practical and theoretical gems. He recorded his ideas in articles, many of which were never published at all.

We might also consider the case of quantum theory, which has proven hugely reliable and useful and yet it may be that NOBODY fully understands it, not even its inventors.

At a more banal level I have considerable experience of theories in immunology that are understood by almost nobody but which are usefully applied. When I introduced the use of rituximab therapy for rheumatoid arthritis I was the only person who fully understood the theory on which that was based. Others in my research group had a good understanding of many aspects but would not claim to have understood the theory in full. The treatment worked and is now widely used. Hardly anybody knows why they are using it, except that it works.

In my experience peer review is pretty much a waste of time. Come to think of it I think that was what the creator of Researchgate thought!

@Jonathan:

I agree with this but I suppose it depends on the type of scientific endeavour.

If falsifiability is the principal criterion for judging the worth of a theory, that suggests that communicability supersedes predictive ability. But if talking about more deductive types of investigation then I'm more inclined to agree with your view that communicability is less important than predictive ability.

@Artur, I also disagree that communicability is a necessary characteristic for what constitutes science

No, Marcel, I am not thinking in terms of black box. I think this question has common ground with your question about perception. We interrogate theories in two ways, as Popper said. We interrogate them by testing their predictions against observations. We also interrogate them in terms of the validity of the internal arguments on which the theory is built. For instance, in neuroscience there are a lot of theories about consciousness that do not actually make the predictions they are said to make. Those predictions could only be made from a different theory. The theories of light up until 1900 assumed that light was either particles or waves. That assumption had no grounding. Leibniz told us that but everybody else ignored him. The correct theory required someone to say that light is composed of indivisible units that are neither particle nor wave but show certain apparent properties of both in different contexts.

You are asking for someone to understand fully their theory, and I think that means that they will understand all the correct internal arguments. So this is not black box. When I predicted the benefit of a certain therapy I did this on the basis of a theory with 55 clearly defined internal steps. I had concluded that the alternative theories involved internal arguments that would not actually go through. Where they said 'if A then B and therefore C ...' I concluded that it would not be C but D so the finding of C could not support this theory.

Quantum theory says all there is to say, it seems. There are no hidden variables. The problem lies in whether or not the internal arguments in the theory are sound. The fact that some people think quantum theory cannot be consistent with general relativity suggests that there may be some false arguments somewhere, even if every time you make a prediction it turns out right.

So I agree with Peter that this is an issue that is of different relevance to different types of theory.

Dear Artur,

On the contrary I am suggesting that I may have been one of very many people more or less in this situation at least for a certain length of time. Take someone like EO WIlson. I suspect that nobody except him fully understands his theory of evolution of eusocial species. Many people understand much of it. Many other people miss the main arguments. However, I suspect that there will be situations where if people are asked what Wilson's theory would predict in a new situation, after everyone making their predictions Wilson might say 'but no actually my theory would predict something different because you have not factored in this particular mathematical parameter'. He might then demonstrate, correctly, the mistake, but nobody might understand simply because of the complexity of the analysis. In biology it is very easy to generate incorrect predictions from a theory.

So I am not going in to metaphysics in any of these examples - I am talking about testable predictions based on mathematical calculations. I am not sure what an uncommunicable statement would be but I am very familiar with ideas that are very hard to communicate because listeners do not have the background experience in modelling the relevant dynamics in their heads and simply lose the plot.

I should clarify that I'm not suggesting that in practice it is possible to have a purely deductive theory. But some are more deductive, and thus less reliant on communicability, than others

Dear Marcel,

I refer to both listeners to oral presentations and readers. Let me give an example.

For the last 15 years I have been proposing that autoimmune diseases mostly arise through the random generation of mutations in antibody genes that give rise to antibodies that perpetuate their own production through a feedback loop. In a hundred or so lectures and a score of articles, chapters and reviews I have introduced this idea by giving the background fact, accepted by all immunologists, that all antibodies arise through random mutation. Normally useful ones are selected and unwanted ones destroyed. Yet if you ask almost any immunologist who has heard of my hypothesis they are likely to say that it is ridiculous to suggest that autoimmune disease occurs just through some random mutation. 'What would cause such an abnormal mutation?' they ask. (On one occasion this provided the basis for an 'expert' witness statement in a patent case.) They appear to completely forget that all antibodies are generated by mutation and that autoantibodies will arise from exactly the same sort of mutation as other antibodies. This is not a theory of some strange cancerous phenomenon outside the rules of immunology. Yet most of my colleagues still do not see how uncontroversial the idea should be, perhaps because they are wedded to some other idea. Only last month a very eminent friend stood up after me and said that I might be right that some antibodies are produced at random but that sometimes they are produced to order in vaccination. They failed to notice that they were themselves fully aware that antibodies produced during vaccination are also produced at random - and then selected!

People are not actually that good at thinking through complex dynamic ideas - particularly in biology. I made lots of mistakes over the years and still find mistakes I continue to make. The intriguing thing is that almost everyone reading this post will understand the point about the random mutation - because they do not suffer from preconceptions. The only person to point out a flaw in argument that I deliberately left in a paper in New England Journal of Medicine for political reasons was a Wall Street analyst with no training in immunology. The capacities of human minds are limited at the conceiving level, and perhaps most limited by preconceivings, I fear. I am not sure it is 'brightness' that is needed either - it may have more to do with scepticism about the received wisdom.

I hadn't seen that but it looks an intelligent review. The autoimmunity hypothesis holds that the system crashes much as a computer might if a 'string' that should be treated as data (the variable region of an antibody gene) functions as a command instead. Very likely there are neural equivalents in psychiatric disease.

Dear Jonathan,

If you don't feel offended, your therapy story and its success do not constitute scientific knowledge. It seems medieval quackery where certain treatment by physicians worked wonders, while they did not know themselves why a particular treatment worked. They applied a knowledge they received from their master or guru. Unless a treatment is not fully understood in its cause and effect by others it is simply a quackery, and their a number of quakes in my country who daily show such miracles. I am sorry for hurting you.

Dear Mohammad,

I am sure I will not offend you either by saying that seems a remarkably muddled set of arguments. That these doctors do not have scientific knowledge was the whole point of my story.

But you seem to confuse knowing why something works with knowing that it works. If you drive a car you turn the key to start it because you have reliable evidence from every day for ten years that it will start if you do that. You probably have little idea how the key turning works. Modern medicine is distinguished from quackery on the basis that it has been shown to work in reliable trials. That has absolutely nothing to do with knowing why or how it works. In general knowing how drugs work has been a very recent phenomenon since about 1980. Prior to that we knew that drugs like aspirin and penicillin worked but not why. The doctors who use rituximab do so because of randomised controlled trials and not with the scientific theory that led me to instigate those trials, and quite right too. There are lots of drugs that should work in theory but in practice are useless or worse.In fact quacks are much more likely to tell you why their treatment works than those following an evidence base.